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For questions on divisors and multiples, mainly but not exclusively of integers, and related and derived notions such as sums of divisors, perfect numbers and so on.

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Help with R. Ryan's "A simpler dense proof regarding the abundancy Index."

I'm reading Richard Ryan's article "A simpler dense proof regarding the abundancy index" and got stuck in his proof for Theorem 2. The Theorem is stated as follows: Suppose we have a fraction of the f …
jvkloc's user avatar
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Help with R. Ryan's "A simpler dense proof regarding the abundancy Index."

It is actually possbile to show that $b$ is odd with a direct proof, without the contradiction I didn't understand. From the assumptions $n$ odd and $I(b)=\frac{\sigma(b)}{b}=\frac{2n-1}{n}$ with an o …
jvkloc's user avatar
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